GLE & CCSS Alignment Updated 7/11/2011 Grade 8 – Unit 1 – Patterns in Number
COVERING BOTH GLE’S AND CCSS (State correlation is not a perfect match-What makes them the same….what makes them different?) 2.1.1 Compare and order rational and common irrational numbers; e.g., -5, 1⁄16, -4½, Ö2, pi; and locate them on number lines, scales and coordinate grids. CC.8.NS.1 Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational. CC.8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2 (square root of 2), show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
2.1.2 Identify perfect squares and their square roots; e.g., squares 1, 4, 9, 16… to corresponding roots 1, 2, 3, 4 …; and use these relationships to estimate other square roots. CC.8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2 (square root of 2), show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
2.2.6 Calculate the square roots of positive integers using technology. CC.8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2 (square root of 2), show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. CC.8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
2.2.11 Use the rules for exponents to multiply and divide with powers of 10 and extend to other bases.
102 × 103 = 105 – Add exponents
25 ÷ 27 = 2-2 – Subtract exponents
CC.8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3(–5) = 3(–3) = 1/(33) = 1/27. CC.8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
2.1.3 Red and represent whole numbers and those between zero and one in scientific notation (and vice versa) and compare their magnitudes. CC.8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.
2.2.7 Develop and use strategies for multiplying and dividing with numbers expressed in scientific notation using the commutative and associative properties. CC.8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
COVERING BOTH GLE’S AND CCSS AND SCIENCE INTEGRATION – N/A
GLE’s but not CCSS 2.1.1 Compare and order rational and common irrational numbers; e.g., -5, 1⁄16, -4½, Ö2, pi; and locate them on number lines, scales and coordinate grids. CC.6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
2.2.5 Compute (using addition, subtraction, multiplication and division) and solve problems with positive and negative rational numbers. CC.7.NS.1b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. CC.7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. CC.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. CC.7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. CC.7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts. CC.7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers. CC.7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) CC.7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
2.2.13 Solve problems in context that involve repetitive multiplication; e.g., compound interest, depreciation; using tables, spreadsheets and calculators to develop an understanding of exponential growth and decay. CC.9-12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
CCSS but not GLE’s – None
Grade 8 – Unit 2 – Patterns in Algebra
COVERING BOTH GLE’S AND CCSS (State correlation is not a perfect match-What makes them the same….what makes them different?) 1.3.10 Evaluate and simplify algebraic expressions, equations and formulas including those with powers using algebraic properties and the order of operations CC.8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. CC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
1.3.12 Write and solve multistep equation using various algebraic methods including the distributive property, e.g., 3 (x + 2) = 10, combining like terms, e.g., 3x + 2x = 15, and properties of equality and justify the solutions. CC.8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). CC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
COVERING BOTH GLE’S AND CCSS AND SCIENCE INTEGRATION – N/A
GLE’s but not CCSS 1.1.1 Generalize the relationships in patterns in a variety of ways including recursive and explicit descriptions; e.g., the pattern 1, 4, 7, 10… is represented as follows:
Recursively as “add 3 to the previous number”
Explicitly as 3n + 1
1.3.10 Evaluate and simplify algebraic expressions, equations and formulas including those with powers using algebraic properties and the order of operations CC.6.EE.2c Evaluate expressions by substituting values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2. CC.6.EE.3 Apply the properties of operations as strategies to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply properties of operations to y + y + y to produce the equivalent expression 3y. CC.6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. CC.7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
1.3.12 Write and solve multistep equation using various algebraic methods including the distributive property, e.g., 3 (x + 2) = 10, combining like terms, e.g., 3x + 2x = 15, and properties of equality and justify the solutions. CC.6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. CC.7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
CCSS but not GLE’s – None
Grade 8 – Unit 3 – Side and Angle Relationships
COVERING BOTH GLE’S AND CCSS (State correlation is not a perfect match-What makes them the same….what makes them different?) 3.1.2 Make and test conjectures about the angle and side relationships to determine that similar figures have congruent angles and corresponding sides proportional and congruent figures have congruent angles and sides. CC.8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. CC.8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
3.1.3 Construct and/or examine right triangles and make and test conjectures about the relationships of the angles and sides and develop the Pythagorean Theorem. CC.8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
3.1.4 Apply side and angle relationships in geometric figures to solves problems including the Pythagorean theorem and similar figures. CC.8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so. CC.8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. CC.8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
3.2.5 Use a coordinate plane to make and test conjectures about changes in the coordinates of the vertices of polygons as a result of a transformation (translation and/or reflection) and describe the results in writing. CC.8.G.1 Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. CC.8.G.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
COVERING BOTH GLE’S AND CCSS AND SCIENCE INTEGRATION – N/A
GLE’s but not CCSS 3.1.1 Determine the effect of scale factors (resulting in similar figures) on the perimeters and areas of two-dimensional shapes and the surface areas and volumes of three-dimensional solids. CC.7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
3.1.3 Construct and/or examine right triangles and make and test conjectures about the relationships of the angles and sides and develop the Pythagorean Theorem. CC.7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
3.3.8 Understand and describe in writing that measurement tools, measurements and estimates of measures are not precise and can affect the results of calculations.
CCSS but not GLE’s – None
Grade 8 – Unit 4 – Ratio, Proportion, and Percentage
COVERING BOTH GLE’S AND CCSS (State correlation is not a perfect match-What makes them the same….what makes them different?) 2.1.4 Represent fractions, decimals, mixed numbers and percentages in equivalent forms. CC.8.NS.1 Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.
COVERING BOTH GLE’S AND CCSS AND SCIENCE INTEGRATION – N/A
GLE’s but not CCSS 2.1.4 Represent fractions, decimals, mixed numbers and percentages in equivalent forms. CC.4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. CC.7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
2.2.9 Use proportional reasoning to write and solve problems in context. CC.7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour. CC.7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
3.3.10 Solve customary or metric measurement problems in context using Dimensional Analysis (The Unit Factor Method) and justify the results in writing. CC.5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step real world problems. CC.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
2.2.10 Solve a variety of problems in context involving percents, including the following:
Percentage of a number, e.g., If 65 percent of the 250 applicants will be accepted to the Arts Magnet School, how many students will be accepted?
The percentage one number is of another number, e.g., Find the percent of students who play soccer if 39 students play soccer out of a total of 387 students.
The percentage of a missing amount, e.g., 5 percent of the money from a fundraiser will be donated to a charity. If $25 is donated to the charity, how much money was made from the fundraiser?
Percentage increase/decrease, e.g., The number of music downloads have increased from 1,345 per minute to 1,567 per minute. What is the percent increase?
CC.6.RP.3c Find a percentage of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percentage. CC.7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
2.2.8 Estimate reasonable answers and solve problems in context involving rational and common irrational numbers, ratios and percentages (including percentage of increase and decrease) and justify solutions in writing. CC.6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.) CC.6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? CC.7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
CCSS but not GLE’s – None
Grade 8 – Unit 5 – Surface Area and Volume
COVERING BOTH GLE’S AND CCSS (State correlation is not a perfect match-What makes them the same….what makes them different?) 3.2.7 Develop formulas using measurement strategies and concrete models; and use formulas to determine the volumes of pyramids, cones and spheres. CC.8.G.9 Know the formulas for the volume of cones, cylinders and spheres and use them to solve real-world and mathematical problems.
3.3.9 Use estimation and measurement strategies, including formulas, to solve surface area and volume problems in context. CC.8.G.9 Know the formulas for the volume of cones, cylinders and spheres and use them to solve real-world and mathematical problems.
COVERING BOTH GLE’S AND CCSS AND SCIENCE INTEGRATION – N/A
GLE’s but not CCSS
3.2.6 Develop and use formulas to determine the surface areas of rectangular prisms, cylinders and pyramids. CC.7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
3.2.7 Develop formulas using measurement strategies and concrete models; and use formulas to determine the volumes of pyramids, cones and spheres. CC.7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms
3.3.9 Use estimation and measurement strategies, including formulas, to solve surface area and volume problems in context. CC.5.MD.5b Apply the formulas V =l×w×h and V = b×h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems. CC.5.MD.5c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. CC.7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
3.3.8 Understand and describe in writing that measurement tools, measurements and estimates of measures are not precise and can affect the results of calculations.
CCSS but not GLE’s – None
Grade 8 – Unit 6 – Patterns and Functions
COVERING BOTH GLE’S AND CCSS (State correlation is not a perfect match-What makes them the same….what makes them different?) 1.1.2 Determine whether relationships are linear or nonlinear. CC.8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. 1.2.5 Represent linear and nonlinear mathematical relationships with verbal descriptions, tables, graphs and equations (when possible). CC.8.F.5 Describe qualitatively the functional relationship between two quantities by reading a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. CC.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. CC.8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
1.1.4 Examine and make comparisons in writing between linear and non-linear mathematical relationships including y = mx, y = mx2 and y = mx3 using a variety of representations. CC.8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. CC.8.F.5 Describe qualitatively the functional relationship between two quantities by reading a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
1.1.3 Write and solve problems involving proportional relationships (direct variation) using linear equations (y = mx). CC.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
1.2.5 Represent linear and nonlinear mathematical relationships with verbal descriptions, tables, graphs and equations (when possible). CC.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. CC.8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. CC.8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. CC.8.F.5 Describe qualitatively the functional relationship between two quantities by reading a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
1.2.6 Determine the constant rate of change in a linear relationship and recognize this as the slope of a line. CC.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. CC.8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. CC.8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
1.2.7 Compare and contrast the slopes and the graphs of lines that have a positive slope, negative slope, zero slope, undefined slope, slopes greater than one and slopes between zero and one. CC.8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
1.2.8 Compare and contrast the slopes and graphs of lines to classify lines as parallel, perpendicular or intersecting. CC.8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
1.2.9 Interpret and describe slope and y-intercepts from contextual situations, graphs and linear equations. CC.8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. CC.8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. CC.8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
1.3.11 Examine systems of two linear equations in context that have a common solution, i.e. point of intersection, using tables, graphs and substitution and interpret the solution. CC.8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. CC.8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. CC.8.EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. CC.8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
COVERING BOTH GLE’S AND CCSS AND SCIENCE INTEGRATION – N/A
GLE’s but not CCSS 1.1.3 Write and solve problems involving proportional relationships (direct variation) using linear equations (y = mx). CC.7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
1.2.5 Represent linear and nonlinear mathematical relationships with verbal descriptions, tables, graphs and equations (when possible). CC.7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
1.2.6 Determine the constant rate of change in a linear relationship and recognize this as the slope of a line. CC.7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
CCSS but not GLE’s – None
Grade 8 – Unit 7 – Making Decisions with Statistics
COVERING BOTH GLE’S AND CCSS (State correlation is not a perfect match-What makes them the same….what makes them different?) 4.2.5 Make predictions from scatter plots by using or estimating a line-of-best-fit. CC.8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. CC.8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
4.2.6 Make observations and inferences and evaluate hypotheses based on collected and/or experimental data. CC.8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. CC.8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
COVERING BOTH GLE’S AND CCSS AND SCIENCE INTEGRATION – N/A
GLE’s but not CCSS 4.1.1 Collect, organize and display data using an appropriate representation (including box-and-whisker plots, stem and leaf plots, scatter plots, histograms) based on the size and type of data set and purpose for its use. CC.6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
4.1.2 Use appropriate representations to compare and analyze large data sets.
4.1.3 Identify where measures of central tendency and spread are found in graphical displays including box-and-whisker plots, stem and leaf plots, scatter plots and histograms. CC.7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
4.2.4 Use descriptive statistics, including range, mode, median, mean, quartiles and outliers to describe data and support conclusions in writing. CC.6.SP.5 Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.
4.2.7 Describe in writing the accuracy of statistical claims, e.g., 4 out of 5 dentists prefer Brand X toothpaste, by recognizing when a sample is biased or when data is misrepresented.
4.2.8 Explain the effects of sample size and sampling techniques (convenience sampling, voluntary response sampling, systematic sampling and random sampling) on statistical claims. CC.7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
CCSS but not GLE’s – None
Grade 8 – Unit 8 – Permutations and Combinations
COVERING BOTH GLE’S AND CCSS (State correlation is not a perfect match-What makes them the same….what makes them different?) None
COVERING BOTH GLE’S AND CCSS AND SCIENCE INTEGRATION – N/A
GLE’s but not CCSS 4.3.9 Determine when a situation is a permutation (changing the order results in a different outcome) or a combination (changing the order does not result in a different outcome).
4.3.10 Use tree diagrams, lists or the Counting Principle to determine all possible outcomes in permutations and combinations.
4.3.11 Apply permutations and combinations to predict possible outcomes and find probabilities to solve problems in a variety of contexts.
Grade 8 Curriculum Work
Looking at our present GLE pacing units in connection with the new CCSS for the purpose of transitioning without gaps or overlaps.Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
All Units in One File
GLE & CCSS Alignment
Updated 7/11/2011
Grade 8 – Unit 1 – Patterns in Number
(State correlation is not a perfect match-What makes them the same….what makes them different?)
2.1.1 Compare and order rational and common irrational numbers; e.g., -5, 1⁄16, -4½, Ö2, pi; and locate them on number lines, scales and coordinate grids.
CC.8.NS.1 Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.
CC.8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2 (square root of 2), show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
2.1.2 Identify perfect squares and their square roots; e.g., squares 1, 4, 9, 16… to corresponding roots 1, 2, 3, 4 …; and use these relationships to estimate other square roots.
CC.8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2 (square root of 2), show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
2.2.6 Calculate the square roots of positive integers using technology.
CC.8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2 (square root of 2), show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
CC.8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
2.2.11 Use the rules for exponents to multiply and divide with powers of 10 and extend to other bases.
- 102 × 103 = 105 – Add exponents
- 25 ÷ 27 = 2-2 – Subtract exponents
CC.8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3(–5) = 3(–3) = 1/(33) = 1/27.CC.8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
2.1.3 Red and represent whole numbers and those between zero and one in scientific notation (and vice versa) and compare their magnitudes.
CC.8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.
2.2.7 Develop and use strategies for multiplying and dividing with numbers expressed in scientific notation using the commutative and associative properties.
CC.8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
2.1.1 Compare and order rational and common irrational numbers; e.g., -5, 1⁄16, -4½, Ö2, pi; and locate them on number lines, scales and coordinate grids.
CC.6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
2.2.5 Compute (using addition, subtraction, multiplication and division) and solve problems with positive and negative rational numbers.
CC.7.NS.1b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
CC.7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
CC.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.
CC.7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
CC.7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.
CC.7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.
CC.7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
CC.7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
2.2.13 Solve problems in context that involve repetitive multiplication; e.g., compound interest, depreciation; using tables, spreadsheets and calculators to develop an understanding of exponential growth and decay.
CC.9-12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
Grade 8 – Unit 2 – Patterns in Algebra
(State correlation is not a perfect match-What makes them the same….what makes them different?)
1.3.10 Evaluate and simplify algebraic expressions, equations and formulas including those with powers using algebraic properties and the order of operations
CC.8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
CC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
1.3.12 Write and solve multistep equation using various algebraic methods including the distributive property, e.g., 3 (x + 2) = 10, combining like terms, e.g., 3x + 2x = 15, and properties of equality and justify the solutions.
CC.8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
CC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
1.1.1 Generalize the relationships in patterns in a variety of ways including recursive and explicit descriptions; e.g., the pattern 1, 4, 7, 10… is represented as follows:
1.3.10 Evaluate and simplify algebraic expressions, equations and formulas including those with powers using algebraic properties and the order of operations
CC.6.EE.2c Evaluate expressions by substituting values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2.
CC.6.EE.3 Apply the properties of operations as strategies to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply properties of operations to y + y + y to produce the equivalent expression 3y.
CC.6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
CC.7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
1.3.12 Write and solve multistep equation using various algebraic methods including the distributive property, e.g., 3 (x + 2) = 10, combining like terms, e.g., 3x + 2x = 15, and properties of equality and justify the solutions.
CC.6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
CC.7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Grade 8 – Unit 3 – Side and Angle Relationships
(State correlation is not a perfect match-What makes them the same….what makes them different?)
3.1.2 Make and test conjectures about the angle and side relationships to determine that similar figures have congruent angles and corresponding sides proportional and congruent figures have congruent angles and sides.
CC.8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
CC.8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
3.1.3 Construct and/or examine right triangles and make and test conjectures about the relationships of the angles and sides and develop the Pythagorean Theorem.
CC.8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
3.1.4 Apply side and angle relationships in geometric figures to solves problems including the Pythagorean theorem and similar figures.
CC.8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so.
CC.8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
CC.8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
3.2.5 Use a coordinate plane to make and test conjectures about changes in the coordinates of the vertices of polygons as a result of a transformation (translation and/or reflection) and describe the results in writing.
CC.8.G.1 Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
CC.8.G.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
3.1.1 Determine the effect of scale factors (resulting in similar figures) on the perimeters and areas of two-dimensional shapes and the surface areas and volumes of three-dimensional solids.
CC.7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
3.1.3 Construct and/or examine right triangles and make and test conjectures about the relationships of the angles and sides and develop the Pythagorean Theorem.
CC.7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
3.3.8 Understand and describe in writing that measurement tools, measurements and estimates of measures are not precise and can affect the results of calculations.
Grade 8 – Unit 4 – Ratio, Proportion, and Percentage
(State correlation is not a perfect match-What makes them the same….what makes them different?)
2.1.4 Represent fractions, decimals, mixed numbers and percentages in equivalent forms.
CC.8.NS.1 Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.
2.1.4 Represent fractions, decimals, mixed numbers and percentages in equivalent forms.
CC.4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
CC.7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
2.2.9 Use proportional reasoning to write and solve problems in context.
CC.7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.
CC.7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
3.3.10 Solve customary or metric measurement problems in context using Dimensional Analysis (The Unit Factor Method) and justify the results in writing.
CC.5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step real world problems.
CC.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
2.2.10 Solve a variety of problems in context involving percents, including the following:
- Percentage of a number, e.g., If 65 percent of the 250 applicants will be accepted to the Arts Magnet School, how many students will be accepted?
- The percentage one number is of another number, e.g., Find the percent of students who play soccer if 39 students play soccer out of a total of 387 students.
- The percentage of a missing amount, e.g., 5 percent of the money from a fundraiser will be donated to a charity. If $25 is donated to the charity, how much money was made from the fundraiser?
- Percentage increase/decrease, e.g., The number of music downloads have increased from 1,345 per minute to 1,567 per minute. What is the percent increase?
CC.6.RP.3c Find a percentage of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percentage.CC.7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
2.2.8 Estimate reasonable answers and solve problems in context involving rational and common irrational numbers, ratios and percentages (including percentage of increase and decrease) and justify solutions in writing.
CC.6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)
CC.6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
CC.7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Grade 8 – Unit 5 – Surface Area and Volume
(State correlation is not a perfect match-What makes them the same….what makes them different?)
3.2.7 Develop formulas using measurement strategies and concrete models; and use formulas to determine the volumes of pyramids, cones and spheres.
CC.8.G.9 Know the formulas for the volume of cones, cylinders and spheres and use them to solve real-world and mathematical problems.
3.3.9 Use estimation and measurement strategies, including formulas, to solve surface area and volume problems in context.
CC.8.G.9 Know the formulas for the volume of cones, cylinders and spheres and use them to solve real-world and mathematical problems.
3.2.6 Develop and use formulas to determine the surface areas of rectangular prisms, cylinders and pyramids.
CC.7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
3.2.7 Develop formulas using measurement strategies and concrete models; and use formulas to determine the volumes of pyramids, cones and spheres.
CC.7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms
3.3.9 Use estimation and measurement strategies, including formulas, to solve surface area and volume problems in context.
CC.5.MD.5b Apply the formulas
V =l×w×h and V = b×h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.
CC.5.MD.5c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
CC.7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
3.3.8 Understand and describe in writing that measurement tools, measurements and estimates of measures are not precise and can affect the results of calculations.
Grade 8 – Unit 6 – Patterns and Functions
(State correlation is not a perfect match-What makes them the same….what makes them different?)
1.1.2 Determine whether relationships are linear or nonlinear.
CC.8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
1.2.5 Represent linear and nonlinear mathematical relationships with verbal descriptions, tables, graphs and equations (when possible).
CC.8.F.5 Describe qualitatively the functional relationship between two quantities by reading a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
CC.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
CC.8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
1.1.4 Examine and make comparisons in writing between linear and non-linear mathematical relationships including y = mx, y = mx2 and y = mx3 using a variety of representations.
CC.8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
CC.8.F.5 Describe qualitatively the functional relationship between two quantities by reading a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
1.1.3 Write and solve problems involving proportional relationships (direct variation) using linear equations (y = mx).
CC.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
1.2.5 Represent linear and nonlinear mathematical relationships with verbal descriptions, tables, graphs and equations (when possible).
CC.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
CC.8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
CC.8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
CC.8.F.5 Describe qualitatively the functional relationship between two quantities by reading a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
1.2.6 Determine the constant rate of change in a linear relationship and recognize this as the slope of a line.
CC.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
CC.8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
CC.8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
1.2.7 Compare and contrast the slopes and the graphs of lines that have a positive slope, negative slope, zero slope, undefined slope, slopes greater than one and slopes between zero and one.
CC.8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
1.2.8 Compare and contrast the slopes and graphs of lines to classify lines as parallel, perpendicular or intersecting.
CC.8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
1.2.9 Interpret and describe slope and y-intercepts from contextual situations, graphs and linear equations.
CC.8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
CC.8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
CC.8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
1.3.11 Examine systems of two linear equations in context that have a common solution, i.e. point of intersection, using tables, graphs and substitution and interpret the solution.
CC.8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
CC.8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
CC.8.EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
CC.8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
1.1.3 Write and solve problems involving proportional relationships (direct variation) using linear equations (y = mx).
CC.7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
1.2.5 Represent linear and nonlinear mathematical relationships with verbal descriptions, tables, graphs and equations (when possible).
CC.7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
1.2.6 Determine the constant rate of change in a linear relationship and recognize this as the slope of a line.
CC.7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Grade 8 – Unit 7 – Making Decisions with Statistics
(State correlation is not a perfect match-What makes them the same….what makes them different?)
4.2.5 Make predictions from scatter plots by using or estimating a line-of-best-fit.
CC.8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
CC.8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
4.2.6 Make observations and inferences and evaluate hypotheses based on collected and/or experimental data.
CC.8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
CC.8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
4.1.1 Collect, organize and display data using an appropriate representation (including box-and-whisker plots, stem and leaf plots, scatter plots, histograms) based on the size and type of data set and purpose for its use.
CC.6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
4.1.2 Use appropriate representations to compare and analyze large data sets.
4.1.3 Identify where measures of central tendency and spread are found in graphical displays including box-and-whisker plots, stem and leaf plots, scatter plots and histograms.
CC.7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
4.2.4 Use descriptive statistics, including range, mode, median, mean, quartiles and outliers to describe data and support conclusions in writing.
CC.6.SP.5 Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.
d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.
4.2.7 Describe in writing the accuracy of statistical claims, e.g., 4 out of 5 dentists prefer Brand X toothpaste, by recognizing when a sample is biased or when data is misrepresented.
4.2.8 Explain the effects of sample size and sampling techniques (convenience sampling, voluntary response sampling, systematic sampling and random sampling) on statistical claims.
CC.7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
Grade 8 – Unit 8 – Permutations and Combinations
(State correlation is not a perfect match-What makes them the same….what makes them different?)
None
4.3.9 Determine when a situation is a permutation (changing the order results in a different outcome) or a combination (changing the order does not result in a different outcome).
4.3.10 Use tree diagrams, lists or the Counting Principle to determine all possible outcomes in permutations and combinations.
4.3.11 Apply permutations and combinations to predict possible outcomes and find probabilities to solve problems in a variety of contexts.